Bayesian modification indices for IRT models

Bayesian modification indices are presented that provide information for the process of model evaluation and model modification. These indices can be used to investigate the improvement in a model if fixed parameters are re-specified as free parameters. The indices can be seen as a Bayesian analogue to the modification indices commonly used in a frequentist framework. The aim is to provide diagnostic information for multi-parameter models where the number of possible model violations and the related number of alternative models is too large to render estimation of each alternative practical. As an example, the method is applied to an item response theory (IRT) model, that is, to the two-parameter model. The method is used to investigate differential item functioning and violations of the assumption of local independence.